Details

Time bar (total: 41.6s)

sample497.0ms

Algorithm
intervals
Results
196.0ms87×body1280valid
135.0ms64×body640valid
94.0ms30×body320valid
20.0ms65×body80valid
7.0ms10×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03250
17450
218150
365650
4315750
done500050

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize99.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.0b
(- (cos x) (cos y))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
16×*-un-lft-identity
12×associate-*r*
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/
9×flip3-- flip--
8×add-cube-cbrt add-log-exp
7×associate-*l* difference-of-squares
6×sub-neg
5×sqrt-prod
4×distribute-rgt-in frac-times distribute-lft-in pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
2×times-frac diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 94
Calls
4 calls:
176.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
83.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms
(- 3.0 (sqrt 5.0))
12.0ms
(- (cos x) (cos y))

series461.0ms

Counts
4 → 10
Calls
4 calls:
224.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
146.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
91.0ms
(- (cos x) (cos y))

simplify1.8s

Counts
104 → 104
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02381837
16461782
228931629
done50001621

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize101.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.4b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- (cos x) (cos y))

rewrite436.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
16×add-exp-log *-un-lft-identity add-cbrt-cube
14×associate-*r/
12×associate-*r*
11×pow1
10×add-cube-cbrt
8×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×sub-neg times-frac prod-exp cbrt-unprod difference-of-squares
4×distribute-rgt-in frac-times distribute-lft-in pow-prod-down associate-*l/ sqrt-prod associate-/r/
3×flip3-+ flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv div-exp frac-add *-commutative associate-/l/ unswap-sqr
1×frac-2neg diff-log clear-num associate-/r* div-inv diff-cos
Counts
4 → 106
Calls
4 calls:
137.0ms
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
180.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
100.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms
(- (cos x) (cos y))

series3.6s

Counts
4 → 12
Calls
4 calls:
3.1s
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
236.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
151.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
101.0ms
(- (cos x) (cos y))

simplify913.0ms

Counts
118 → 118
Iterations

Useful iterations: done (905.0ms)

IterNodesCost
03664085
111103990
done50003491

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize157.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (sin x) (/ (sin y) 16.0)))
0.6b
(cbrt (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.0b
(- (cos x) (cos y))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
14×*-un-lft-identity
12×cbrt-prod
8×add-log-exp
7×difference-of-squares
6×add-cube-cbrt
4×pow1 add-exp-log cbrt-div flip3-- add-cbrt-cube flip-- distribute-lft-out--
2×sub-neg times-frac pow1/3 diff-log
1×sqrt-prod diff-cos
Counts
4 → 62
Calls
4 calls:
28.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
23.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
14.0ms
(- 3.0 (sqrt 5.0))
17.0ms
(- (cos x) (cos y))

series671.0ms

Counts
4 → 10
Calls
4 calls:
283.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
282.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
105.0ms
(- (cos x) (cos y))

simplify2.2s

Counts
72 → 72
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0168998
1362967
2875901
32820878
done5000860

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize149.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- (cos x) (cos y))
1.6b
(- (sqrt 3.0) (sqrt (sqrt 5.0)))

rewrite385.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
18×*-un-lft-identity
15×sqrt-prod
12×associate-*r*
11×pow1 add-exp-log add-cbrt-cube difference-of-squares
10×associate-*r/
9×flip3-- flip--
8×add-cube-cbrt add-log-exp
7×associate-*l*
6×sub-neg
5×distribute-lft-out--
4×distribute-rgt-in frac-times distribute-lft-in pow-prod-down prod-exp cbrt-unprod
2×times-frac diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 99
Calls
4 calls:
214.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
119.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
17.0ms
(- (cos x) (cos y))
27.0ms
(- (sqrt 3.0) (sqrt (sqrt 5.0)))

series529.0ms

Counts
4 → 10
Calls
4 calls:
257.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
165.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
106.0ms
(- (cos x) (cos y))
0.0ms
(- (sqrt 3.0) (sqrt (sqrt 5.0)))

simplify2.3s

Counts
109 → 109
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02281917
16051852
227631693
done50021687

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes475.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03569
14569
done4569

end0.0ms

sample18.2s

Algorithm
intervals
Results
10.0s2793×body1280valid
5.0s1802×body640valid
1.3s752×body320valid
919.0ms2310×body80valid
324.0ms343×body160valid